Shortcuts don't work after restart
Update: In Blender 2.81 you will be able to use 1, 2 and 3 for switching vertex, edge and face select even when your keymap is based on the Industry Compatible keymap. The operator is now decoupled from the specific keymap. It's using object.mode_set_with_submode as operator instead of ic_keymap.mesh_select_mode. This change was added with commit rB23d19c2b0dd3f47339ef07be39d47c41848be39b.



The reason this issue occurs is because the industrial keymap registers an operator called IC_KEYMAP_OT_mesh_select_mode which provides the functionality to switch between selection modes for vertices, edges and faces. However this registration happens only when the industrial keymap is loaded / selected in the preferences. A custom keymap based on the industrial keymap doesn't trigger this, resulting in a shortcut referencing an operator that doesn't exist. However if you open your preferences after restarting Blender and switch to the industrial keymap and then back to your custom keymap, it will have the operator registered because you have loaded the industrial keymap before.